"""
请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）


注意：

一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。
空白格用 '.' 表示。


示例 1：


输入：board =
[["5","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
输出：true
示例 2：

输入：board =
[["8","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。


提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字（1-9）或者 '.'
"""
from typing import List


class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:

        # 确定位置
        """
        数独的坐标是 9*9
        根据位置判断区域
        需要 rows 和 columns 和，3 * 3 的数组一个
        遍历所有数组，然后对出现次数进行累加
        """
        rows_flag = [[0 for i in range(9)] for j in range(9)]
        columns_flag = [[0 for i in range(9)] for j in range(9)]
        subboxes = [[[0] * 9 for j in range(3)] for k in range(9)]
        for i in range(0, 9):
            for j in range(0, 9):

                if board[i][j] != '.':
                    # 判断横轴的坐标
                    rows_flag[i][int(board[i][j]) - 1] += 1
                    # 判断纵轴的坐标
                    columns_flag[j][int(board[i][j]) - 1] += 1
                    # 判断这个点在那个区域
                    subboxes[int(i / 3)][int(j / 3)][int(board[i][j]) - 1] += 1
                    if rows_flag[i][int(board[i][j]) - 1] > 1 or columns_flag[j][int(board[i][j]) - 1] > 1 or subboxes[int(i / 3)][int(j / 3)][int(board[i][j]) - 1] > 1:
                        return False

        return True


if __name__ == '__main__':
    board = [["5","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
    solution = Solution()
    print(solution.isValidSudoku(board))
